{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1)Autocovariance Function(AF)\n",
    "时间序列与其滞后项的协方差\n",
    "\n",
    "X为随机变量（即随着时间变化取值随机的变量,比如股票价格）,E表示求数学期望,u是随机变量X的均值\n",
    "\n",
    "\n",
    "$AF_k=E[(X_t-\\mu _t)(X_{t-k}-\\mu_{t-k})]=Cov(X_t,X_{t-k})$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了消除量纲影响：<br>\n",
    "2)Autocorrelation Coefficient Function（ACF）\n",
    "$ACF_k=\\frac{Cov(X_t,X_{t-k})}{Var(X_t)}$<br>\n",
    "\n",
    "但是这样会出现一个这样的现象，咱们以计算股票价格的实现序列数据为例：<br>\n",
    "假设你研究的是今天的价格与昨天的价格的相关性，但是时间序列又是全部关联在一起的（也就是假设在一阶相关的情况下，今天的股票价格与昨天相关，但是昨天的价格也与前天相关，前天的股票价格又与大前天相关，以此类推，这样我们考察的相关性已经不是单纯的“今天价格”与“昨天价格”的相关性了，而是包含一系列价格信息综合影响），所以为了剔除之前其他交易日的价格信息的影响，单纯研究某一天（或者某一时期的价格）对今天的价格影响，我们引入Partial Autocorrelation Coefficient Function<br>\n",
    "\n",
    "3）Partial Autocorrelation Coefficient Function(PACF)<br>\n",
    "$PACF_t=Corr(X_t,X_{t-k}|X_{t-1},X_{t-2},X_{t-(k-1)})$\n",
    "\n",
    "但是这个只是数学的表达，并未说明如何计算，我们将每一个时间序列中的$X_k$进行表达：<br>\n",
    "$X_t=\\Phi_{k1}X_{t-1}+\\Phi_{k2}X_{t-2}+......\\Phi_{kk}X_{t-k}+\\mu_t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import tushare as ts\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "token='09e4ce601d278a47514902d805936146d469550c6ec9c3b42d1d2343'\n",
    "pro=ts.pro_api(token)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pro.index_daily(ts_code=\"000001.SH\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.index=pd.to_datetime(df.trade_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=df.sort_index()[-250:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "our_df=df.close"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "our_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.tsa.api as smt\n",
    "fig = plt.figure(figsize=(10, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "acf=smt.stattools.acf(our_df,nlags=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pacf=smt.stattools.pacf(our_df,nlags=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "acf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.context('bmh')\n",
    "# plt.style.context('ggplot')\n",
    "fig = plt.figure(figsize=(10, 8))\n",
    "layout = (3,1)\n",
    "ts_ax = plt.subplot2grid(layout, (0, 0))\n",
    "acf_ax = plt.subplot2grid(layout, (1, 0))\n",
    "pacf_ax = plt.subplot2grid(layout, (2, 0))\n",
    "data.plot(ax=ts_ax)\n",
    "ts_ax.set_title('Stock Price Time Series Data')\n",
    "smt.graphics.plot_acf(data, lags=30, ax=acf_ax, alpha=0.5)\n",
    "acf_ax.set_title('Autocorrelation Coefficient')\n",
    "smt.graphics.plot_pacf(data, lags=30, ax=pacf_ax, alpha=0.5)\n",
    "pacf_ax.set_title('Partial Autocorrelation Coefficient')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们需要对时间序列数据进行预测，我们需要选取平稳的时期，因为时间序列可能会有大的“性质改变”，这样之前我们建立的模型就会失效，所以我们引入平稳性（Stationary）的概念："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.时间序列的均值和方差为常数，因此其时序图应该围绕某一水平线上下以大致相同的幅度波动。如果该时序图存在明显递增、递减或周期性波动，则该时间序列很可能是不平稳的\n",
    "2.自相关或偏自相关系数一般会快速减小至0附近或者在某一阶后变为0，而非平稳的时间序列的自相关系数一般是缓慢下降而不是快速减小\n",
    "3.单位根检验:\n",
    "1)Dickey-Fuller Test、Augmented Dickey-Fuller Test、Phillips-Perron Test"
   ]
  },
  {
   "attachments": {
    "randomwalk.jpg": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![randomwalk.jpg](attachment:randomwalk.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "白噪音是一种完全随机的序列，也就是说在时间序列的任意一个时间t，都有\n",
    "$E(X_t)=0 \\; Var(X_t)=\\sigma ^2 \\; ACF_k=0$\n",
    "各变量独立并且都服从正态分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$x_t = x_{t-1}+\\varepsilon_t$<br>\n",
    "$x_0=0,\\varepsilon_{t} \\sim N(0,\\sigma_{\\varepsilon}^2)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m--------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                    Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-72a0ba22bf33>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;31m#使用numpy简单模拟白噪声过程\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mseed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0;31m# plot of discrete white noise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0mrandser\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m500\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as scs\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.tsa.api as smt\n",
    "def ts_plot(data, lags=None,title=''):\n",
    "    if not isinstance(data, pd.Series):   \n",
    "        data = pd.Series(data)\n",
    "    with plt.style.context('bmh'):    \n",
    "        fig = plt.figure(figsize=(10, 8))\n",
    "        layout = (3, 2)\n",
    "        ts_ax = plt.subplot2grid(layout, (0, 0))\n",
    "        acf_ax = plt.subplot2grid(layout, (1, 0))\n",
    "        pacf_ax = plt.subplot2grid(layout, (1, 1))\n",
    "        qq_ax = plt.subplot2grid(layout, (2, 0))\n",
    "        pp_ax = plt.subplot2grid(layout, (2, 1))\n",
    "\n",
    "        data.plot(ax=ts_ax)\n",
    "        ts_ax.set_title(title+'time series plot')\n",
    "        smt.graphics.plot_acf(data, lags=lags, ax=acf_ax, alpha=0.5)\n",
    "        acf_ax.set_title('ACF')\n",
    "        smt.graphics.plot_pacf(data, lags=lags, ax=pacf_ax, alpha=0.5)\n",
    "        pacf_ax.set_title('PACF')\n",
    "        sm.qqplot(data, line='s', ax=qq_ax)\n",
    "        qq_ax.set_title('QQ plot')        \n",
    "        scs.probplot(data, sparams=(data.mean(), data.std()), plot=pp_ax)\n",
    "        pp_ax.set_title('PP plot') \n",
    "        plt.tight_layout()\n",
    "    return\n",
    "\n",
    "#使用numpy简单模拟白噪声过程\n",
    "np.random.seed(1)\n",
    "# plot of discrete white noise\n",
    "randser = np.random.normal(size=500)\n",
    "ts_plot(randser, lags=30,title='white noise')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(8)\n",
    "\n",
    "random_data_array = np.random.normal(size=250)\n",
    "\n",
    "random_data_series = pd.Series(random_data_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c1eddfe10>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "plt.style.context('bmh')\n",
    "fig = plt.figure(figsize=(10, 3))\n",
    "\n",
    "random_data_series.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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e3wTaUDGt0v+V7am2rGLU56rvtZYrftdjt8lsKrR94L9waIRnDhyaUNnRf8hFhYq9qVLIlIKgPPSCo8sVDzuDkcKRQ1Brf4VCsHnHPrbvfo6lJx/Pyp65dHQ0YJfNLIW2D/znh0b4zeBzzW6G5UihEHzqB1vp37WfoeECXTM6OGP+bD568XKHvjWVr9KpoVAI7n90L9++f4D7H91LwcfkNkGbd+yjf9d+Dg4XCODgcIH+XfvZvGNfs5tmOdf2e/iT4T00q8f23c8xNDz6MpOh4QLbdz/HuUtObFKrpj93k9XPgV9F+R4ajN5D8x+sjWfpycfTNaPj8PoD0DWjg6UnH9/EVk1v3gnLhrt0qhhrD81sPCt75nLG/NkwPARRYGYSTit75ja7adOWu8my4cCvorSHVi6ve2g+l5FeR4f46MXLmf3Qd5n1bz/hfRcu855oFWnWLe+EZcNdOlWU9tC2PPY0dM5g5jEzcrmH5sPoyevoEF27+2F3P+cu+YtmN6flpF233E2WDe/hV+E9tCIfRlujpF233E2WDQd+DaU9tFmP/pRzl5yYu7AHH0Zb46Rdt7wTlg136VhNPow+Io+XBGY1z9WmM5l1q127yaotn0Zx4LeYVgoWn8soyuO5jLHmGZjwOlprOle/7mVet6i9fL77Zxc0ZN1y4LeQVguW0mH0n77/Q4zMXsBV716fiz3bSnm8L6PWPN//2F7+ecuTE15Ha03nwcd/63WL2svn7l/v4rUrTsm8Pvfht5AsT5JmdTll3s5lVFtueTyXUWue73lkd6p1dKxll7d1q5pay2frzmcbUp/38FtIVrfkt9qRwmQ0o2ur1nJbc9YpuTuXUauPHUi1jvo80NhqLZ/lC+c0pD7v4TdJtT3JrG74mu6XU5aC9/o7H+Zb9w1w/Z0P86kfbG34TV+1lhtQ85LArI6kWu0Gt1qXQZ7/4pNTraO+nHJstZbP6pfOb0h93sNvgkafyJqKh3c1cg98Mn3mWbSn1nJ7bM/zVfubgUyOpFrxiKzW+Rsg1Trq80Bjq7V8Ohu0fBz4TdDoE1ljHUZnEYyNDqi0G6ys2jPWcqt2SeD9j+7N5GTuVJ0UTvvd17oMMu062q6XU9aS1XJuBAd+E4wXaPV++bUup3z5ohdlEoyNDqi0/b5ZtSftZahZHUlN1RFZVhvpvAV4Gq14tFYukz58SWskbZPUL+nqKu/PlHRr8v4mSUuzqHe6yvLhbNX6fmvdlfjg47/NpG+/0VetpO33zao9ae/mzOp7nIqH9U338zrTRasv57oDX1IncANwMbACWCdpRUWxK4G9EXEG8Dngr+qtN61WOimW1YmssU5uVrvkLatgbHRANSt4S3VP9FLBrL7HqTixmcdLS5uh1Zezos5f1Zb0SuCTEfG6ZPgjABHx6bIytydlfiZpBvAk0B1jVH7SkuXx2o/eNKk2bf75ZgBWnr2S4ULw3MFDPLbnAAcOjRABEsw6ppPTTpqFVPsP+uGHfgnAshW/M6l2jCUi+HX/I9DZxcKFpzJ7Zufhtky03mdfGObxfQdG/TC6BIvmzmLOsTOOms545WupnE5E8NieAzx/8BAg1KHDyxNg/8ERXjg0wrHHdI6ar1rLoVb5iS6HsdozVt0Tnd+xxmfxPY43nbSqLdP9B0cy+e7HG9+s6TRDI5fzCcceM+l23fbu370vInqrvZdF4F8GrImIdybDbwPOi4irysr8MikzkAz/JinzdMW01gPrAWaf+pJXXPKJm+tqG8BwIXjqmRdSBeN40q68Wayk1QLh6f1DPL1/6Kiy3bO7mDdnZtVpjLXhSxtQ+w+OcPDQCDOTlR0YM3jTbDjSboirtWe84G1WeGQZchNdpj0nHsuOvS9k8t1nOW/VTGbjl9Xf5ETHN3o5t3Lgvwl4XUXgr4qI95aV2ZKUKQ/8VRGxu9Z0e3t7o6+vr662Aex5bohPb9zKt+4boHxOBVz2isW88dzFvOctawG44RsbJjTNWuXTjp+oUtdN5cnENWedwhfu6h91cnPmjA7ed+Gy1JcvFgpR99VB9z+6l+vvfLhmeyqXw3jla2n099VoWbW/2ntjLdOVPXNrXj2S1bJo1Lo+3knPrP4mJzq+0cv5vNNPmvRJXkk1Az+Lk7YDQE/Z8GJgZ60ySZfOi4A9GdQ9IdP9F6xKJ4KY0QXqOOqGoJkzOhBMqO+3o0Ocu+RE3nju4sN91KU/sv0r3sCB01816Rud0vZfTkV/Z6EQDJ18BgeWXND0czdTYbxHGVR+962m1ro+1knPWt9xI7/7ySznVlgXs7gs815gmaTTgceBy4G3VJTZAFwB/Ay4DLhzrP77rJVOilVeKjVd7vYb74ageq+rH/VHxuQva0x7OWWjb7sv35DROYPr73y4pS6Ra4TJLNNSEI3MXsD9j+5t6o1Rk70Ho/I7vvp1L+Mzt/+qYd992uXcKuti3Xv4ETEMXAXcDmwFbouILZKulbQ2KfYl4GRJ/cAHgaMu3Wyk0lUf77twGZe9YvGoqz5aYas7nrGOULLYa8tqT7u0YZ3oEUfa8mlNZm+x0bJc36pNK+0yzeroLitpj8Zrfcff2fx4Q7/7tMu5VdbFTG68ioiNwMaKcdeUvX4BeFMWdU1WKRjL9xJaZas7nkYfoWS1p13asE70iCNt+bSm4oamNLJc38aaVpplmtXRXVbSruu1vuNtTz2b+rtPc6STdt1tlXUx13fattrKXkujgzHLDUq1DWuW5dNotSc1Zrm+jTetiS7TVgmikrTreq3v+MwFc0bdfV0an2WXS5p1t1XWxVwH/mRW9mb1dzYyGBu9QWmWVjt3k2W4ZjWtVgmicmnW9Vrf8R+tXMS2p56d8Hff6J2/VlkXcx340/XESyM0coPSLGNtyJqx4c4yXLOaVqsE0WSN9R2n+e4bfaTTKjtVuQ78tCv7dOkCakWtdGTUrA13luGa1bRaJYjqUWtnJc13P9aP3GS17rbCTlWuA3+6nniZblrtyKhZG+4swzXraTU7iKZKre+es6i6AS09YbZV1t165TrwYXqeeJluWu3IqJkb7izDNU9BnZW097S02rpbL//EYQqNvm68XbXaEwSn+53XNnlp72lptXW3Xrnfw0+jHfo7m6HVjoym+4lKm7y0332rrbv1cuCnVOswutaJnVa6bb1ZWi1gveHOr7Tffautu/Vy4GegWc/zmC6yDNh2umLCmiPNd99uOwcO/AzUOrEz6nkeTP8TPvXIImBb7WqfqeAjxOZrp50Dn7TNwGSe52HptcoDqKZKqz3YzKY/B34Gap35P3PBHF8NkqF2u2JiPHnbwFnjOfAzUOtyzT9auciXcWYob5dT5m0DZ43X9n34HeKokKiteKhc+mmWSF6PjHMIPZnneVh67XbFxHja7ZJAa762D/y5x3XxiiVddU+nUAgKERQCChFlG4Xi6wDOPm1usUzhSLlCBC+ZP/vw69IGpDQtqL4xKd/oVI6rWr7GdGpNN2250nzCkfkvbhBrT7DWO5HM95FpTGw6nZ3iY5cs54Ed+9j+dPtvQPO2gbPGa/vAz0pHhyh2zFiz/e4Z84iyje9IIdmQJhvV8YwqEqM32sX3o+x1xWcZvSWuVa68fCGO7DCMJDsD1eqottH+7GUvp2/7Hn4z+Bynzzuec3pOBDFqx6K0sRyvLWYOfJuWJNEp6EQc09ns1jTWWQtfNGV1lR9plW84yo/mxtpQzT52BhGw4tQTOFQoMDwSHBopMFyIUUfG5d2nh4/yShveZENeu41lG9LS0WZ5u6uUrzWvMcb77ciBb2aHSSp7fdS7Y352pBC8cOJLGDp+AX2P7mH1mfPpnCbdbRFHH+VB9Y1baaNU3s2Zqq4JtKVR3ZQOfDOr20gheNuXNjG47A+Jjhm895sPsLJnLjdfed60CH1JFRu41m/zZPiyTDOr293bdrF5xz6is3jPwPNDI2zesY+7t+1qdtOsjAPfzOq2ZeczHBgaGTXuwNAID+18pkktsmoc+GZWt7MWnsCsrtFnz2d1dbJi4QlNapFV48A3s7qtPnM+K3vmclxXJwKO6+pkZc9cVp85v9lNszI+aWtmdevsEDdfeR53b9vFQzufYcXCE6bVVTp5UVfgSzoJuBVYCmwH3hwReyvKrAT+FjgBGAGui4hb66nXzFpPZ4e4aPkCLlq+oNlNsRrq7dK5GrgjIpYBdyTDlZ4H3h4RZwFrgM9L8r3hZmZTrN7AvxT4avL6q8AbKgtExK8j4uHk9U5gF9BdZ71mZpZSvYG/ICKeAEj+H/MMjaRVQBfwmxrvr5fUJ6lvcHCwzqaZmVm5cfvwJf0LcEqVtz6WpiJJpwI3A1dERKFamYi4EbgRoLe3N0dPuDAza7xxAz8iXlPrPUlPSTo1Ip5IAr3qbXWSTgD+Cfh4RNwz6daamdmkaaznkI/7Yemvgd0R8RlJVwMnRcSHK8p0AT8AvhcRn08x7UHg0Uk3DuYBT9fx+enG89ve8ja/kL95zmp+l0RE1fOk9Qb+ycBtwGnAY8CbImKPpF7g3RHxTklvBb4MbCn76DsiYvOkK55Y2/oioreRdbQSz297y9v8Qv7meSrmt67r8CNiN3BRlfF9wDuT118DvlZPPWZmVj8/WsHMLCfaOfBvbHYDppjnt73lbX4hf/Pc8Pmtqw/fzMymj3bewzczszIOfDOznGi7wJe0RtI2Sf3JvQFtR9JNknZJ+mXZuJMk/UjSw8n/JzazjVmS1CPpLklbJW2R9P5kfFvOs6RjJf2rpJ8n8/uXyfjTJW1K5vfW5B6XtiGpU9IDkr6fDLf7/G6X9AtJmyX1JeMauk63VeBL6gRuAC4GVgDrJK1obqsa4isUnzxabiJPLp2uhoEPRcRy4HzgPcn32q7zfBC4MCLOBlYCaySdD/wV8LlkfvcCVzaxjY3wfmBr2XC7zy/AqyNiZdn19w1dp9sq8IFVQH9EPBIRQ8AtFJ/o2VYi4sfAnorR4z65dLqKiCci4v7k9bMUQ2ERbTrPUbQ/GTwm+RfAhcC3kvFtM78AkhYDfwD8XTIs2nh+x9DQdbrdAn8RsKNseCAZlwepnlw6XUlaCpwDbKKN5znp3thM8flUP6L4hNl9ETGcFGm3dfvzwIeB0oMVT6a95xeKG/EfSrpP0vpkXEPX6Xb7icNqv6fm607bhKTZwD8AH4iIZ4o7ge0pIkaAlcmPBX0HWF6t2NS2qjEkvR7YFRH3SVpdGl2laFvMb5kLImKnpPnAjyT9qtEVttse/gDQUza8GNjZpLZMtaeSJ5aWHkVd9cml05WkYyiG/dcj4tvJ6LaeZ4CI2AfcTfHcxVxJpZ20dlq3LwDWStpOsRv2Qop7/O06v8DhH4QiInZR3KivosHrdLsF/r3AsuTsfhdwObChyW2aKhuAK5LXVwD/2MS2ZCrpz/0SsDUi/kfZW205z5K6Sz8DKmkW8BqK5y3uAi5LirXN/EbERyJicUQspfg3e2dE/DFtOr8Ako6XNKf0Gvj3wC9p8DrddnfaSrqE4t5BJ3BTRFzX5CZlTtI3gdUUH6f6FPAJ4LtUeXJps9qYJUm/B/wE+AVH+ng/SrEfv+3mWdLLKZ6w66S4U3ZbRFwr6cUU94BPAh4A3hoRB5vX0uwlXTp/HhGvb+f5TebtO8ngDOAbEXFdrScQZ1ZvuwW+mZlV125dOmZmVoMD38wsJxz4ZmY54cA3M8sJB76ZWU448M3McsKBb2aWE/8fIS8OTvw2SwcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "smt.graphics.plot_acf(random_data_series, lags=50)"
   ]
  },
  {
   "cell_type": "code",
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